J. Earth Syst. Sci. (2019) 128:84 c© Indian Academy of Scienceshttps://doi.org/10.1007/s12040-019-1098-5

Review on estimation methods of the Earth’s surfaceenergy balance components from ground and satellitemeasurements

Md Masudur Rahman1,2 and Wanchang Zhang1,*1Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy ofSciences, Beijing 100 094, People’s Republic of China.2University of Chinese Academy of Sciences, Beijing 100 049, People’s Republic of China.*Corresponding author. e-mail: zhangwc@radi.ac.cn

MS received 20 June 2017; revised 17 March 2018; accepted 19 July 2018; published online 22 March 2019

Accurate estimation of the Earth’s surface energy balance (SEB) components is very much important forcharacterising the environmental, hydrological and bio-geophysical processes to predict the weather andclimate or climate change. This narrative review summarises the basic theories of estimation methodsof the solar (shortwave) radiation, thermal (longwave) radiation and evapotranspiration (latent heatflux) from both the ground and satellite measurements, which are inherently complex to measure atlarge scale. This paper discusses the reviews of prior and recent advances in the estimation methods andmodels by focusing their advantages, disadvantages and recommendations. Uncertainties associated withsatellite estimations and some key directions for further studies are also discussed, including the statusof ground-based measurements at regional and global scales and the advent of new satellite technologiesfor quantifying the SEB components more accurately. This study infers that the further advances in thesatellite remote sensing and worldwide ground-based measurement networks will enhance the capabilitiesfor the potential estimation of the SEB parameters as well as monitoring the global water and energycycles to develop significant environmental studies for the betterment of living on the Earth.

Keywords. The Earth’s surface; energy balance; solar radiation; thermal radiation; evapotranspiration;estimation methods.

1. Introduction

Sun is the primary source of energy on Earth. Theincoming solar radiation is distributed in differ-ent components due to the scattering, reflecting,transmitting and absorbing characteristics of theEarth’s surface and atmosphere. The net radia-tion is partitioned into sensible heat flux, latentheat flux and soil heat flux i.e. known as thesurface energy balance (SEB) which is extremelyvital to any land surface models for developing

the hydrological, ecological and bio-geophysicalprocesses. The very basic equation of SEB can beexpressed as

Rn = G + H + LE, (1)

where Rn is the net radiation in W m−2, G is thesoil heat flux, H is the sensible heat flux and LEis the latent heat flux. The land surface radiationbudgets, i.e., the Earth’s SEB between the incom-ing radiation in both short and longwave spectra

1

0123456789().,--: vol V

84 Page 2 of 22 J. Earth Syst. Sci. (2019) 128:84

are characterised by the net radiation (Rn) whichcan be expressed as

Rn = Rsn + Rl

n, (2)

Rsn = (1 − α)Rs↓, (3)

Rln = εRl↓ − εσT 4

s , (4)

where Rs ↓ and Rl ↓ are the incoming radiationof both shortwave (solar) and longwave (ther-mal) spectra, respectively, α is the albedo (unitless), ε is the atmospheric emissivity (unit less),Ts is the surface temperature (K) and σ is theStefan–Boltzmann constant (W m−2 K−4). Nowthe sensible heat flux (H) and latent heat flux (LE)can be written in the following equations:

H = ρ CpdT

rah, (5)

LE = Rn − G − H, (6)

where ρ is the air density (kg m−3), Cp is the airspecific heat (J kg−1 K−1), dT is the tempera-ture difference between air and surface (K) and rah

is the aerodynamic resistance (s m−1). The abovesaid components of Earth’s SEB are responsible forheating or cooling of the land/soil (solar and ther-mal radiation), the heating and cooling of the air(sensible heat flux) and the evaporation of waterfrom soil and vegetation (latent heat flux). Figure 1shows an illustration of the Earth’s surface radia-tion and energy flow among the space, atmosphereand Earth’s surface.

Figure 1 shows that the incoming solar radi-ation is reflected and absorbed by the clouds,atmosphere and Earth’s surface after that thecloud, atmosphere and Earth’s surface emit thethermal radiation along with the other turbulent(soil, sensible and latent heat) fluxes. The netabsorbed radiation plays a vital role in the envi-ronmental analysis and it should be zero, if notthen heating effect for positive value and coolingfor negative. To illustrate the energy flows at aglobal and local view, there were a lot of iconicdiagrams that have been presented in the pub-lished articles and textbooks (Wild et al. 2009;Stephens and L’Ecuyer 2013; L’ecuyer et al. 2015)based on the conceptual background and sev-eral satellite and ground measurements. Trenberthet al. (2009) revealed the measurement of meanEarth’s energy budget by a satellite sensor theClouds and the Earth’s Radiant Energy System

(CERES) for the March 2000 to May 2004 periodand found that the net absorbed radiation was0.9 W m−2, which simply infers today’s globalwarming issues.

Nowadays, there are more frequent weatheranomalies as a consequence of global warming.Due to the interlinked systems, changes in sin-gle aspect of global process reverberate throughthe entire system, e.g., increasing surface tempera-tures modify the rainfall patterns and evaporationrates, which may lead to floods, droughts andstorms, and hurricanes may intense due to theincrease in sea surface temperatures. This is thecommon scenario over several parts of the worldand has become an important research question.The study of energy flows between the Earth’ssurface, the atmosphere and space is of greatimportance for different types of environmentalanalysis (Krishnamurti and Biswas 2006; Wangand Liang 2008; Yingying et al. 2008; Xie et al.2016), including climate change, disaster moni-toring, plant water demand, plant growth, pro-ductivity, the irrigation management system andalso in determining the large-scale atmosphereand ocean circulation patterns which eventuallydrive weather and climate (Slingo and Slingo 1988;Hartmann 1994; Lee et al. 2001; Schumacher et al.2004; Bonan 2008). Therefore, we can feel thatthe effective estimation of land surface radia-tion and energy components is factually neces-sary for the Earth and environmental analysisto predict the weather and climate or climatechange. However, the estimation of these com-ponents is very complex in nature due to thediverse characteristics of the atmosphere andEarth’s surface.

To the best of our knowledge, the number of pub-lished review articles related to this review workis limited but the existing papers have presentedvery good and critical review works (Diak et al.2004; Li et al. 2009; Liang et al. 2010; Nouri et al.2013; Liou and Kar 2014; Shi et al. 2015; Zhanget al. 2016, etc.), which are reflecting the excellentstate of art in the estimation techniques of surfaceenergy fluxes. They reviewed the estimation meth-ods of surface flux components in terms of history,measurement methods, merits and demerits of themethods and also focused on some experimentalresults. Most of the studies focused on one compo-nent such as evapotranspiration (ET, latent heatflux) based on the satellite estimation techniques,whereas we focus on the three important compo-nents (solar radiation, thermal radiation and ET)

J. Earth Syst. Sci. (2019) 128:84 Page 3 of 22 84

Figure 1. The conceptual diagram of the Earth’s SEB phenomena among the space, atmosphere and the Earth’s surface.

based on both the ground and satellite estimationtechniques. The SEB has four main components asshown in equation (1), the net radiation (Rn) isthe combined calculation of solar (shortwave) andthermal (longwave) radiation, the sensible (H) andlatent (LE) heat fluxes are the results of atmo-spheric turbulences and soil/ground heat flux (G)which can be calculated as the function of netradiation, soil and vegetation characteristics (Bas-tiaanssen et al. 1998a, b). So, the estimation ofnet radiation using the solar and thermal radia-tions and estimation of any other heat flux usingenergy balance approach will have to go throughthe indirect estimation of all SEB components.As the energy balance is not closed (Foken 2008),therefore indirect estimation of a SEB componentmay lead to errors and uncertainties. Hence, the

individual estimation of sensible heat flux (H) andsoil heat flux (G) can be studied further.

This study explains the fundamental andadvanced estimation techniques of SEB compo-nents in more concise words and equations whencompared with other reviews. However, an impor-tant purpose of this paper is to provide an overallidea to a reader, who is not specialist in this field.The meanings of all used symbols in this study areindicated in table 1 for quick reference. Along withthe main concepts, advantages, disadvantages anduncertainties, we make some recommendations tothe readers/researchers, where one can apply thesemethods. This paper aims to review the recentdevelopment in the estimation methods and mod-els of three basic components of the Earth’s SEBsuch as solar radiation, thermal radiation and the

84 Page 4 of 22 J. Earth Syst. Sci. (2019) 128:84

Table 1. The used symbols and their respective meanings.

Symbols Meanings

α Surface albedo

γ Psychrometric constant

ε Atmospheric emissivity

Δ Slope of saturated vapour pressure

ΔT Vertical difference of temperature

Δq Vertical difference of water vapour concentration

Δz Vertical distance between two measurement points

λ Latent heat of evaporation/vapourisation

ρ Density of air

ρdry Density of dry air

ρv Density of water vapour

ρv Fluctuation in water vapour density

ρwet Density of wet/moist air

σ Stefan–Boltzmann constant

B Bowen ratio

C2n Refractive index fluctuation of air

Cp Specific heat of air at constant pressure

DEM Digital elevation model

dT Temperature difference between air and surface (temperature

gradient)

e Actual vapour pressure

esat Saturated vapour pressure

Ein Received radiation at the pyrgeometer/sensor surface

Em Measured radiation at the pyrgeometer/sensor surface

Eout Emitted radiation at the pyrgeometer/sensor surface

EF Evaporative fraction

EFr Relative evaporative fraction

ET Evapotranspiration

ETa Actual evapotranspiration

ETdry Evapotranspiration at dry reference pixel

ETr Reference evapotranspiration

ETwet Evapotranspiration at wet reference pixel

fc Fractional vegetation cover

G Ground/soil heat flux

H Sensible heat flux

Hc Canopy sensible heat flux

Hdry Sensible heat flux at dry reference pixel

Hs Soil sensible heat flux

Hwet Sensible heat flux at wet reference pixel

KH Coefficient of sensible heat transfer

KV Coefficient of latent heat transfer

LA Leaf area index

LE Latent heat flux

LEdry Latent heat flux at dry reference pixel

LEwet Latent heat flux at wet reference pixel

NDVI Normalised vegetation index

P Atmospheric pressure

Rl ↓ Incoming longwave radiation

Rl ↑ Outgoing longwave radiation

Rn Net radiation

Rln Net longwave radiation

Rsn Net shortwave radiation

Rs ↓ Incoming shortwave radiation

J. Earth Syst. Sci. (2019) 128:84 Page 5 of 22 84

Table 1. (Continued.)

Symbols Meanings

Rs ↑ Outgoing shortwave radiation

rah Aerodynamic resistance

rah c Canopy aerodynamic resistance

rah dry Aerodynamic resistance at dry reference pixel

rah wet Aerodynamic resistance at wet reference pixel

rah s Soil aerodynamic resistance

S Sensitivity/calibration factor of instrument

T Absolute temperature of pyrgeometer/sensor detector

T Fluctuation in air temperature

Ta Air temperature

Tc Canopy temperature

TH Maximum surface temperature in dry condition

TLE Minimum surface temperature in wet condition

Trad Directional radiometric surface temperature

Ts Surface temperature/also used as soil temperature

Ts DEM Surface temperature adjusted to a standard elevation per pixel of

the satellite image

U Fluctuation in vertical wind speed

Vemf Output voltage of the pyrgeometer/sensor thermopile

ET, i.e., latent heat flux from satellite and groundmeasurements to achieve the present status andfuture directions in the study area.

2. Solar (shortwave) radiation

The solar radiation is the only significant energysource on the Earth that is transformed intovarious energy fluxes after entering into the atmo-sphere and Earth’s surface. Basically, solar radia-tion has two acting parts: one is incoming(downward Rs↓) radiation on Earth’s surface thatdepends on the atmospheric transmitivity, solarconstant, solar altitude and incidence angle, andanother part is outgoing (upward Rs↑) that is re-flected back to space due to the combined effectof surface, clouds, aerosol, gases, etc. It is a mea-sure of radiation received on a given area in a giventime, usually indicated as the average irradiance inwatts per square metre (W m−2) that engendersin visible (VIS) and near-infrared (NIR) spectra(wavelength of 300–4000 nm).

2.1 Ground measurement of solar radiation

The basic science of solar irradiance is the detec-tion of the optical electromagnetic radiation thatis converted into electric signals, which can bemeasured by conventional techniques. There aretwo types of instruments available for measuringsolar radiation such as pyrheliometer for direct

irradiance and pyranometer for both direct anddiffuse irradiances (Paulescu et al. 2013). Thepyrheliometer is a broadband instrument that mea-sures the direct beam of solar radiation. Thepyranometer is a type of actinometer for measur-ing solar radiation (direct and diffuse) incomingfrom a 2π (360◦) solid angle on a planar sur-face as shown in figure 2. These instruments areclassified with respect to their quality by theInternational Standard ISO 9060/1990 that is alsoadopted by the World Meteorological Organization(WMO) (Guide to Meteorological Instruments andMethods of Observation, Seventh Edition 2008).

However, there are some worldwide and regionalground measurement networks for measuring thesurface flux components as briefly described here.The WMO started the measurement of solar radi-ation from 1964 along with other components forsurface radiation energy balance. The World Radi-ation Data Center (WRDC) is located at theCentral Geophysical Observatory in St. Peters-burg, Russia inside WMO that collects data fromthe large network with more than 1000 stationsfor monitoring solar radiation (Main GeophysicalObservatory, World Radiation Data Center, St.Petersburg, Russia). The Baseline Surface Radi-ation Network (BSRN) (Ohmura et al. 1998) isa project under the umbrella of the World Cli-mate Research Program (WCRP) (World ClimateResearch Programme n.d.) (n.d. stands for no dateor year of publication, i.e., the citation is only

84 Page 6 of 22 J. Earth Syst. Sci. (2019) 128:84

Figure 2. The schematic diagram (left) and photograph (right) of pyranometer (Solar Instruments/Atmospheric ScienceInstruments n.d.).

available on website/Internet) as a part of GlobalEnergy and Water Cycle Exchange (GEWEX)(Global Energy and Water Cycle Exchange n.d.)for land surface radiation measurement with asmall number of stations (currently 59 as ofDecember 2016) covering a latitude range from80◦N to 90◦S (Baseline surface radiation net-work n.d.). The Global Energy Balance Archive(GEBA) is a database established in 1985 atETH Zurich for measuring the monthly meansof surface energy fluxes (Gilgen and Ohmura1999). The Surface Radiation Budget Network(SURFRAD) is a nation-wide network of USNational Oceanic and Atmospheric Administra-tion (NOAA) (Surface Radiation (SURFRAD)Network n.d.) to measure the surface radiationbudgets over the United States since 1993 (Augus-tine et al. 2005). FLUXNET (Baldocchi et al.2001) is a set of regional networks that coordi-nate regional and global analysis to measure theexchange of carbon dioxide (CO2), water vapourand energy between terrestrial ecosystems and theatmosphere based on eddy-covariance method with683 (as of April 2016) sites (FLUXNET A GlobalNetwork n.d.) over seven regions (AmeriFlux,CarboEurope, KoFlux, OzFlux, Fluxnet-Canada,AsiaFlux and ChinaFlux). Some other regional net-works also exist and these networks have a setof stations to cover a desired area but the mat-ter is that how much areas are covered and howthese stations are distributed, i.e., the optimumdistance between two stations. Cros and Wald(2003) showed that a station can cover an areaof ∼30 km. Most of the measuring projects areusing the Kipp and Zonen or Eppley or Huksefluxstandard instruments to ensure the quality datacollection.

2.2 Satellite estimates of solar radiation

Satellite remote sensing techniques are the onlyeffective way to estimate the components of landSEB at both regional and global scales in contrastto the limited ground-based estimations. There hasbeen a firm advancement in estimating the Earth’sradiation budget since the first meteorologicalsatellite was launched in the 1960s. Basically, thesetypes of satellites measure the radiation of differ-ent wavelengths in the electromagnetic spectrum,i.e., collect images of different spectrum such asVIS, NIR, thermal infrared (TIR) and microwaverange as radiation is the form of energy that can betransmitted without any material medium. How-ever, the general procedure of satellite estimates ofthe Earth’s SEB components is outlined in figure 3,which shows that we still need some ground mea-surement. The meteorological and solar radiationdata are used for deriving some models and thesurface energy components for accuracy measure-ments. Researchers are following the above illus-trated procedure for estimating the surface fluxesand trying to use less ground data for deriving theirmethods/models to achieve the high accuracy withrespect to ground measurements.

2.2.1 Satellite sensors

Various broadband radiometric sensors are onboard in multiple satellite spacecrafts – the EarthRadiation Budget (ERB) sensor on Nimbus-7(Jacobowitz and Tighe 1984); the Earth RadiationBudget Experiment (ERBE) sensor on three satel-lites which are NOAA-F, NOAA-G and anotherone with 57◦ inclination orbit which travels aroundthe Earth once every 2 months (Barkstrom and

J. Earth Syst. Sci. (2019) 128:84 Page 7 of 22 84

Figure 3. The flow chart of generalised estimation procedure of the Earth’s SEB components from satellite measurements.

Smith 1986); the Clouds and the Earth’s RadiantEnergy System (CERES) (The Clouds and theEarth’s Radiant Energy System n.d.) sensor whichwas 1st launched on Tropical Rainfall Measure-ment Mission (TRMM) in 1997 including EuropeanSpace Agency’s (EOS) Terra, Aqua and recentlythe Suomi National Polar Orbiting Partnership(S-NPP) (Soumi NPP n.d.); the Advanced Space-borne Thermal Emission and Reflection Radio-meter (ASTER) on Terra in 1999 (The AdvancedSpace-borne Thermal Emission and ReflectionRadiometer n.d.) and the Geostationary EarthRadiation Budget (GERB) sensor on Meteosat-8 and Meteosat-9 launched in 2002 and 2007,respectively (Harries et al. 2005). There are alsosome sensors to produce surface radiation on bothgeostationary and orbiting satellites such as theSpinning Enhanced Visible and Infrared Imager(SEVIRI) on Meteosat Second Generation (MSG)satellite (Schmetz et al. 2002); the AdvancedBaseline Imager (ABI) sensor on GeostationaryOperational Environmental Satellite (GOES) (TheGeostationary Operational Environmental Satel-lite-Advanced Baseline Imager (ABI) n.d.) and

Moderate Resolution Imaging Spectro radiometer(MODIS) on Terra in 1999 and Aqua in 2002(MODIS n.d.). In the case of data accumulation,the calibration of satellite instruments is mostlyimportant but some missions did not have on-board calibration devices, which makes the dataprocessing more complicated and another problemis the time gap like eight years between EREBand CERES. The meteorological satellites are ableto collect the high temporal resolution (hourly)images over a large area, which are then furtherprocessed and compared with ground measure-ments to extract the desired information. It canderive the hourly irradiation most accurately atlocations that are further 25 km away from aground station (Zelenka et al. 1988).

2.2.2 Estimation methods

There are numerous methods for retrieving solarradiation from satellite signals. The developmentof these methods is still on going. At this stage,we can roughly classify these methods into threecategories. First, the look-up-table (LUT) method

84 Page 8 of 22 J. Earth Syst. Sci. (2019) 128:84

is a data structure that is developed based onthe radiative transfer process (Liang et al. 2006;Lu et al. 2010; Huang et al. 2011). This methodis extensively used to achieve high accuracy evenit has some drawbacks such as computationallynot economical and used in limited channel data.Second, the parameterisation methods that esti-mate solar radiation by establishing a model, i.e.,the process of developing parametric equationswith several parameters such as cloud, aerosol, gasand other atmospheric and surface variables (Kimand Ramanathan 2008; Wang and Pinker 2009;Lichun et al. 2015). Sometimes it is hard to keepthe temporal resolution high due to the changingtendencies of some input parameters (e.g., cloudparameters). Third, the statistical method which isdeveloped based on the statistical process and arti-ficial neural network (ANN) that directly link thesatellite observed signals to estimate solar radiationat regional scale (Lu et al. 2011; Hena et al. 2013).The most common disadvantage of these meth-ods is the lack of generalisation. However, manyresearchers utilised the combination of the abovestated methods (Rigollier et al. 2004; Kawai andKawamura 2005; Yeom and Han 2010; Wang et al.2014), which is known as the hybrid method. Thesummary of the above stated methods is listed intable 2.

3. Thermal (longwave) radiation

Longwave radiation is the electromagnetic radia-tion that is being emitted from the Earth’s surfaceand atmosphere as infrared (4–100 µm) at lowenergy in the form of thermal radiation to space.It is measured in W m−2 and mathematicallyexpressed as in equation (4). The longwave radi-ation also has two parts: one is outgoing longwaveradiation (the dominating part) which dependson the land surface characteristics such as sur-face temperature and emissivity and another isthe incoming longwave radiation that depends onthe cloud cover and humidity, i.e., the sky tem-perature and sky emissivity. The incoming solarradiation and outgoing longwave radiation are thekey components of radiation balance. These areextremely important to develop any land surfaceand climate model because the Earth’s surfaceand atmosphere gain energy by absorbing solar(shortwave) radiation, which is known as radia-tive heating, and lose energy by emitting thermal(longwave) radiation to balance the absorption of Table

2.Summary

ofthesatellite-basedestimationmethodsofsolarradiation.

Nam

eofth

em

ethods

and

refe

rence

sM

ain

conce

pts

Adva

nta

ges

Dis

adva

nta

ges

Rec

om

men

dati

ons

Look-u

pta

ble

(LU

T)

(Muel

leret

al.

2009;M

a

and

Pin

ker

2012;Zhang

etal.

2014)

Radia

tive

transf

erm

odel

(RT

M)

base

ddata

stru

cture

Hig

hacc

ura

cy

No

nee

dto

per

form

calc

ula

tion

for

each

pix

el

Com

puta

tionally

not

econom

ical.

The

reca

lcula

tion

ofLU

Tis

ver

y

tim

eco

nsu

min

g.T

he

thre

shold

for

reca

lcula

tion

ishig

h

The

reca

lcula

tion

tim

e/

the

am

ount

ofRT

M

calc

ula

tions

can

be

reduce

d

by

usi

ng

an

eigen

vec

tor

appro

ach

Para

met

eriz

ati

on

(Sunet

al.

2012;Tanget

al.

2016)

Dev

elopin

gpara

met

ric

equati

ons

base

don

sever

al

atm

osp

her

icand

surf

ace

para

met

ers

Com

puta

tionally

cost

effec

tive

Hard

tokee

phig

hte

mpora

l

reso

luti

on

due

toth

e

changin

gte

nden

cyofso

me

input

para

met

ers

An

exte

nsi

ve

erro

ranaly

sis

is

reco

mm

ended

toim

pro

ve

the

acc

ura

cyofsh

ort

wav

e

radia

tive

flux

esti

mati

on

from

MO

DIS

pro

duct

s

Sta

tist

icalm

ethod

(Luet

al.

2011;Y

eom

and

Han

2010)

Sta

tist

icalappro

ach

like

AN

N(a

rtifi

cialneu

ral

net

work

)th

at

dir

ectl

ylink

the

sate

llit

eobse

rved

signal

Sta

ble

and

effici

ent

Sim

ple

alg

ori

thm

Sem

iauto

mate

din

natu

re

Tim

eco

nsu

min

gfo

rhig

h

tem

pora

lre

solu

tion

Hig

hly

reco

mm

ended

for

geo

stati

onary

sate

llit

ew

ith

enhance

dre

vis

itin

gability

J. Earth Syst. Sci. (2019) 128:84 Page 9 of 22 84

solar radiation, also known as radiative cooling(Kiehl and Trenberth 1997). The resultant of thesetwo components is the net radiation that deter-mines the ultimate heating or cooling of globalsystem.

3.1 Ground measurement of thermal radiation

At surface, the longwave radiation is mainly mea-sured by pyrgeometer. It is an electronic devicethat measures near surface infrared radiation spec-trum according to the following mathematical rela-tionships (Pyrgeometer n.d.):

Em = Ein − Eout, (7)

where Em is the measured radiation at the pyr-geometer sensor surface in W m−2, Ein is thelongwave radiation received from the atmosphereand Eout is the longwave emitted by the sensorsurface. Now, the generated radiation at the instru-ment sensor surface can be calculated as

Em =Vemf

S, (8)

Eout = σT 4, (9)

where Vemf is the output voltage of the pyrge-ometer thermopile in volts (V), S is the sen-sitivity/calibration factor of the instrument inV W−1 m−2, σ is the Stefan–Boltzmann constantin W m−2 K−4 and T is the absolute temperatureof pyrgeometer detector in K. Therefore, the long-wave radiation can be calculated as

Ein =Vemf

S+ σT 4. (10)

A schematic diagram and photograph of pyrgeome-ter is shown in figure 4. However, the ground-based

measurement networks as described in previoussection such as BSRN, WRC, GEBA, FLUXNET,SURFRAD, etc. also collect the longwave radia-tion data over their coverage regions. The accuracyof longwave radiation measurement was set to30 W m−2 as per BSRN standard, recent measureddata are more faithful of ±5 W m−2 (1.5%) and thequality check performed by updated BSRN tools(Long and Dutton 2002; Schmithusen et al. 2012).

3.2 Satellite estimates of thermal radiation

Due to the limited coverage and maintenance com-plexity of ground measurements in large scale,the satellite retrieval of longwave radiation is veryimportant for analysing the Earth’s climate sys-tem. The measurement of longwave radiation fluxis affected by the processes of scatterings, absorp-tions and emissions from clouds, aerosols, gases andthe surface. The researchers are developing vari-ous algorithms based on different types of methods,which can be categorised roughly into three.

The first type is known as the empirical methodbased on the empirical functions using satellite-derived meteorological parameters such as surfacetemperature and water vapour burden (Ellingsonet al. 1983; Wang and Liang 2009). This methodwith simple algorithms is sensitive to errors butwidely used in numerous applications. The sec-ond type is the radiative transfer method (RTM;Schmetz 1989; Vazquez-Navarro et al. 2013) thatcalculates the radiation quantities using the atmo-sphere temperature and water vapour profiles, itcan directly measure the downward longwave radi-ation using atmospheric profiles and the upwardlongwave radiation using land surface profiles asit has the strong validity of physics. The thirdtype is known as the hybrid method (Wang and

Figure 4. The schematic diagram (left) and photograph (right) of pyrgeometer (Solar Instruments/Atmospheric ScienceInstruments n.d.).

84 Page 10 of 22 J. Earth Syst. Sci. (2019) 128:84

Liang 2010; Jiao et al. 2015) that is developedbased on the combination of radiative transfersimulation and the statistical approaches such asANN. The hybrid method indicates that there isa good generalisation and also the good accuracy.The summary of the above indicated methods isprovided in table 3.

4. ET (latent heat flux)

ET is the vital component of the Earth SEB that isthe collective value of evaporation from water bod-ies and the transpiration from vegetation and/orany other moisture containing living tissues, i.e.,the processes of losing water from the Earth’s sur-face to the atmosphere by both the evaporation andtranspiration. This component is characterised bythe latent heat flux of the Earth’s surface as math-ematically expressed in equation (6). This processcools the Earth’s surface and moistens the atmo-sphere near surface which is why the estimation ofET is crucial for developing climatic, hydrological,bio-geophysical and ecological models to predictthe weather and climate or climate change. A lot ofefforts have been made for the accurate estimationprocedure of ET as described in this section.

4.1 Ground measurement of ET

The potential ground measurement of ET hasnot been well observed with the common in-situinstruments and methods. Basically, micrometeo-rological measurement-based methods are vastlyimplemented to estimate ET (the latent heat flux)such as Bowen ratio energy balance (BREB),eddy covariance (EC) and Penman–Monteith (PM)method (Gavilan and Berengena 2007; Shi et al.2015). ET can also be estimated based on weighinglysimeter (Gebler et al. 2015), providing the onlydirect measurement of water flux from vegetatedarea, i.e., the lysimeter water balance.

The BREB methodology is developed based onthe SEB equation. The Bowen ratio (Bowen 1926)is defined as the ratio of the sensible heat flux (H)to the latent heat flux (LE) as expressed in thefollowing equation:

B =H

LE=

KHρ CpΔTΔZ

KV λ ΔqΔZ

, (11)

where KH and KV are the coefficient of sensi-ble and latent heat transfer, ρ is the air density,Cp is the air specific heat, λ is the latent heat Table

3.Summary

ofsatellitebasedthermalradiationestimationmethods.

Nam

eofth

em

ethods

and

refe

rence

sM

ain

conce

pts

Adva

nta

ges

Dis

adva

nta

ges

Rec

om

men

dati

ons

Em

pir

icalm

ethod

(Yuet

al.

2014;D

utt

aet

al.

2015)

Em

pir

icalfu

nct

ions

base

d

alg

ori

thm

that

dev

eloped

usi

ng

RS

retr

ieved

atm

osp

her

icpara

met

ers

Sim

ple

alg

ori

thm

and

easy

to

det

erm

ine

the

coeffi

cien

ts

More

erro

rse

nsi

tive

Sig

nifi

cant

posi

tive

erro

rov

erari

d

regio

n

Alg

ori

thm

should

be

retr

ain

edw

ith

more

per

fect

physi

caldefi

nit

ion

in

extr

eme

clim

ate

condit

ions

Radia

tive

transf

erm

ethod

(Zhouet

al.

2007;Park

etal.

2015)

The

radia

tive

transf

er

sim

ula

tion

toca

lcula

teth

e

radia

tion

quanti

ties

usi

ng

the

atm

osp

her

icand

land

surf

ace

pro

file

s

Ithas

the

stro

ng

validity

of

physi

cs

Applica

ble

toall

atm

osp

her

ic

pro

file

s

The

per

form

ance

ofth

ebasi

c

alg

ori

thm

bec

om

edeg

raded

due

toth

eco

mm

on

calc

ula

tion

ofall

sky

Alg

ori

thm

should

be

impro

ved

by

separa

ting

the

calc

ula

tion

for

clea

rand

cloudy

sky

Hybri

dm

ethod

(Yuet

al.

2013;Y

anet

al.

2016)

This

met

hod

dev

eloped

on

the

com

bin

ati

on

ofra

dia

tive

transf

ersi

mula

tion

and

stati

stic

alappro

ach

es

Agood

gen

eraliza

tion

is

obse

rved

inth

ism

ethod

Wid

ely

acc

epte

dfo

rgood

acc

ura

cy

Vari

able

sele

ctio

nfo

rst

ati

stic

al

appro

ach

esis

crit

icaland

cruci

al

Larg

eer

ror

appea

rs,w

her

eth

e

tem

per

atu

reis

hig

hsu

chas

for

barr

enor

des

ert

surf

ace

s

Aco

rrec

tion

met

hod

isre

quir

edfo

r

model

coeffi

cien

tsder

ivati

on

from

the

hig

hgro

und-a

irte

mper

atu

re

diff

eren

ceto

reduce

the

over

esti

mati

on

oflo

ngw

ave

radia

tion

J. Earth Syst. Sci. (2019) 128:84 Page 11 of 22 84

Figure 5. The operational diagram (left) and photograph (right) of the large aperture scintillometer (LAS) MkII ET System(Solar Instruments/Atmospheric Science Instruments n.d.).

of vapourisation, ΔT and Δq are the verticaldifferences of temperature and water vapour con-centration and ΔZ is the vertical distance betweenthe two measurement points. Now equation (6) canbe rewritten as

LE =Rn − G

1 + B. (12)

In equation (12), if we have known B for a certainsystem then LE can be calculated from the mea-sured net radiation (Rn) and soil heat flux (G).

The EC method (Pauwels and Samson 2006; Haet al. 2015) estimates H and LE directly from thefluctuations of wind speed, temperature and watervapour. Observing the covariance between watervapour density and wind speed, we can calculatethe latent heat flux as

LE = λρvU , (13)

where λ is the latent heat of vapour, ρv is the fluc-tuation in water vapour density (kg m−3), U is thefluctuation in vertical wind speed (m s−1) and theoverbar stands to indicate the average operation.Similarly, the sensible heat flux can be calculatedas

H = ρ Cp T U , (14)

where ρ is the density of the surrounding air andT is the fluctuation in air temperature (◦C).

In recent years, the use of scintillometer hasbecome popular for its large area coverage andgood performance (Nieveen and Green 1998; Mei-jninger 2003; Ward and Evans 2015). Scintillometeris an electronic device that measures the sensibleheat flux (H) of the surface and then calculates thelatent heat flux (LE) using other climatic param-eters (net radiation and soil heat flux) based on

the SEB. The basic principle is that it measuresthe turbulent intensity of the refractive index fluc-tuations (C2

n) of air between a collimated lightsource (transmitter) and a detector (receiver). Thetransmitter sends a beam of light (electromagneticradiation) at a known wavelength over a known dis-tance of one to several kilometres and at the endof the path the receiver collects the travelled radia-tion and analyses the fluctuations of the radiationintensity to find out the turbulent heat fluxes. Anoperational diagram and photograph of large aper-ture scintillometer (LAS) is shown in figure 5. Theestimated result of ET using this method showsa good agreement with the remote sensing-basedestimation. Samain et al. (2012) presented the ETrates calculated per 10-day periods. It showed agood agreement between the remote sensing-basedestimation and LAS-derived results with differencefrom 3.5% to 12.6%.

4.2 Satellite estimates of ET

Nowadays, satellite retrieval of ET has become awidespread area of interest to researchers for itshighest cost effectiveness and large area coveragewith revisiting capability as well as the reasonablygood accuracy. The satellite-based estimation ofET started roughly from 1980 and is still develop-ing based on various approaches and methods. It ishard to say which method or approach is the bestbecause every aspect of these approaches/methodshas its own merits and demerits. There are vari-ety of models and methods for ET retrieval fromsatellite data such as the SEB-based methods (Kus-tas 1990), surface temperature vegetation indices(Ts-VI)-based methods (Tang et al. 2009), thePenman–Monteith (PM) method (Zhang et al.2009), Priestley–Taylor (PT) method (Fisher et al.

84 Page 12 of 22 J. Earth Syst. Sci. (2019) 128:84

2008), empirical method (Wang et al. 2007), waterbalance method (Wan et al. 2015) and other meth-ods (Ryu et al. 2011; Wang and Bras 2011). Thesemethods are further simplified and modified toimprove their performance. The significant advan-tage of SEB methods is that these are using theenergy balance approach, which can quantify sur-face fluxes and their water-use dynamics withoutreference to the source of water information asopposed to other models such as water-balancemodel, which requires detailed information of watersources. However, this paper focuses on variousSEB-based methods and models.

4.2.1 Surface energy balance index (SEBI)

The SEBI model is based on the crop water stressindex (CWSI), by scaling up the observed tem-perature in the maximum (max) temperature (drycondition) and the minimum (min) temperature(wet condition) (Jackson et al. 1981), which isthe fundamental concept for all the SEB models.The observed max and min surface temperaturesare interpolated to calculate the relative evapo-rative fraction (EF) then for a particular surfacealbedo and roughness, the pixelwise SEBI com-putes the regional ET from pixelwise max and minsurface temperature redefined CWSI and relativeEF. Due to the complexity in the determination ofthe max and min surface temperatures and pooraccuracy of SEBI, it was further developed witha simplified form named simplified-SEBI (S-SEBI)(Roerink et al. 2000). Here, a reflectance (albedo)-dependent max and min surface temperatures arepointed out to determine the dry and wet con-ditions for partitioning the available energy intosensible and latent heat fluxes. The ET is calcu-lated in terms of EF, which can be defined as theratio of ET/latent heat flux (LE) to the availableenergy (Rn−G). Under the dry and wet conditions,it can be formulated by interpolating the albedo-dependent surface temperatures as

EF =TH − Ts

TH − TLE, (15)

where TH is the max surface temperature at dryconditions and represents the max sensible heatflux and min latent heat flux, TLE is the min sur-face temperature at wet conditions and representsthe max latent heat flux and min sensible heat fluxand Ts is the surface temperature.

4.2.2 Surface energy balance system (SEBS)

The SEBS was developed by Prof Dr Su in theNetherlands in 2002 to estimate the actual ETand other land surface heat fluxes in terms ofatmospheric turbulent fluxes and EF from remotesensing (RS)-based data and some meteorologicalmeasurements (Su 2002; Su et al. 2003). Basically,it is the modified form of SEBI; here, the assump-tions are: the latent heat flux is zero at the drylimit, i.e., the sensible heat flux (Hdry) is maximum(the available energy, Rn − G); on other hand, atwet limit, Hwet reaches at its minimum value asexpressed:

Hdry = Rn − G, (16)

Hwet =(Rn − G)γ

γ + Δ− ρCp (esat − e)

rah (γ + Δ), (17)

γ =CpP

0.622λ, (18)

where γ is the psychrometric constant (k Pa ◦C−1),P is the atmospheric pressure (Pa), Δ is the slopeof saturated vapour pressure as a function of Ta

in k Pa ◦C−1, e and esat are the actual and sat-urated vapour pressures, and rah is dependent onthe Obukhov length which in turn is a function ofthe friction velocity and sensible heat flux. Now therelative evaporative fraction (EFr) and EF can beexpressed as

EFr =Hdry − H

Hdry − Hwet, (19)

EF =EFr ∗ LEwet

Rn − G. (20)

Here, to calculate the heat fluxes a distinctionis made between the planetary boundary layer(PBL)/atmospheric boundary layer (ABL) and theatmospheric surface layer (ASL) to take the ABLheight as a reference of potential air temperature.In SEBS, the parameters are derived from RS dataand ground (meteorological and radiation) data areused as inputs to estimate the sensible heat fluxand EF as well as the other components.

4.2.3 Surface energy balance algorithm for land(SEBAL)

The SEBAL was developed by Prof. Bastiaanssenin the Netherlands in 1998, which is one-layer image processing model (Bastiaanssen et al.

J. Earth Syst. Sci. (2019) 128:84 Page 13 of 22 84

1998a, b). It estimates latent heat flux, i.e., ET asa residual of SEB and other land surface fluxesat both local and regional scales with minimumground-based meteorological data. Basically, thismodel is a moderate approach based on boththe empirical relationship and physical parame-terisation scheme. Here, we need to collect thesatellite imagery data of VIS, NIR, TIR spectraand also the land surface temperature (Ts), nor-malised vegetation index (NDVI) and albedo maps.The latent heat flux (LE) is estimated accord-ing to energy balance equation (6), where the netradiation (Rn) is computed from the balance ofsolar (shortwave) and thermal (longwave) radia-tion as indicated in equation (2), the soil heatflux (G) is calculated by the proposed equation ofBastiaanssen (2000), which is applicable to all cat-egories of vegetation cover and land. The sensibleheat flux (H) is computed according to equation(5), where SEBAL considers a linear relationshipbetween the near surface-air temperature difference(dT ) and the radiometric surface temperature (Ts)assuming the meteorological and surface conditionsare homogeneous as expressed:

dT = cTs + d, (21)

where ‘c’ and ‘d’ are the empirical parametersobtained from the extreme evaporative condition,i.e., the ‘anchor’ pixel (Bastiaanssen 1995) for agiven satellite image. The user can assign thedry/hot pixel and the wet/cold pixel to calculatedT on both conditions as

dTdry =Hdry∗rah dry

ρdry∗Cp, (22)

dTwet =Hwet∗rah wet

ρwet∗Cp. (23)

where rah dry and rah wet are the aerodynamic resis-tances at dry and wet conditions, respectively. Inequation (22), the value of sensible heat flux isassumed to be maximum as Hdry = Rn − G (max-imum available energy) at dry pixel (taken from apixel that located in an area that shows high sur-face temperature). In equation (23), the value ofsensible heat flux Hwet is assumed to be zero at wetpixel (generally taken from a pixel located in deepwater/water body), i.e., dTwet = 0. After determin-ing the value of dT at both wet and dry pixels, thevalues of ‘c’ and ‘d’ in equation (21) can be easilyestimated. By using the values of ‘c’, ‘d’ and respec-tive surface temperature (Ts) of each pixel, the

air-surface temperature difference (dT ) at everypixel is calculated using equation (21). Finally, thevalue of sensible heat flux (H) for each pixel isestimated iteratively with aerodynamic resistancecorrected for stability using equation (5).

This method has been applied for ET estima-tion at both field and catchment scale in more than30 countries such as Spain, Turkey, Egypt, India,Srilanka, China, USA, etc. over the world with anaverage accuracy of 85% (daily) and 95% (seasonal)at field scale (Bastiaanssen et al. 2010).

4.2.4 Mapping evapotranspiration at highresolution with internalised calibration(METRIC)

The METRIC is also an image processing tool(Allen et al. 2007) that is extended from SEBAL.The METRIC considers the slope aspect as Ts

which relapses to Ts DEM (the surface tempera-ture adjusted to a standard elevation per pixel ofthe satellite image) through a common arbitrarydatum, based on the image-specific lapse rate. Thismethod uses the ASCE (American Society for CivilEngineers) standardised reference evapotranspira-tion (ETr), which is calculated using the ASCEPenman–Monteith equation for alfalfa (about 0.5m taller, rougher agricultural crop) field (ASCE-EWRI 2005). Here, the calibration via referenceET is done by choosing the dry pixel as ETdry = 0and the wet pixel as ETwet = 1.05ETr. However,this algorithm still suffers from the subjective spec-ification of extreme pixels, i.e., dry and wet pixelselection.

4.2.5 Two-source model (TSM)

The TSM is also known as dual source model thatwas proposed by Norman et al. (1995) to improvethe ET estimation accuracy from RS data (Sanchezet al. 2007). The basic concept of this model is todivide the composite radiometric temperature intotwo sources: one is soil and another is vegetativecanopy, and to compute the sensible heat flux asthe sum of canopy sensible heat flux (Hc) and soilsensible heat flux (Hs) is expressed as

H = Hc + Hs, (24)

Hc = ρair CpTc − Ta

rah c, (25)

Hs = ρair CpTs − Ta

rah s, (26)

84 Page 14 of 22 J. Earth Syst. Sci. (2019) 128:84

where Tc and Ts are the canopy and soiltemperatures, respectively, Ta is the air temper-ature, and rah c and rah s are canopy and soilaerodynamic resistances, respectively. Here, Tc andTs are related to the directional radiometric surfacetemperature Trad as

Trad =[fc · T 4

c + (1 − fc)4]1/4

, (27)

fc = 1 − exp(−0.5 · Ω · LA

cos θ

), (28)

where fc is the fractional vegetation cover, Ω is afactor that indicates the degree to which the vege-tation is clumped (Kustas and Norman 1999), LA

is the leaf area index and θ is the viewing angleof the radiometer. This model experiences someuncertainties in determining the initial and cor-rected value of the PT coefficients as it utilises thePT parameterisation scheme for energy partition-ing (Yang et al. 2015).

However, there are also some other methods andmodel for mapping regional and local ET such asrecently the NP (non-parametric) approach (Liuet al. 2012; Pan et al. 2016) has been proposed byfew researchers, where the net radiation, surfaceair temperature, land surface temperature and soilheat flux as the inputs without the need of param-eterising resistance. After reviewing the detailedliterature related to the estimation techniques ofET fluxes, we make a summarisation as listed intable 4.

5. Errors and uncertainties associated withsatellite estimations

Several types of errors and uncertainties are foundin satellite estimation of SEB components dueto various problems and limitations in estima-tion methods and models, as well as the unevencharacteristics of the atmosphere and Earth’ssurface. Some important sources of uncertaintiesand possible ways to reduce them are outlinedhere.

(1) Errors associated with surface temperatureretrieved from satellite measurement: In thecase of satellite estimation, most of the meth-ods are using TIR radiation data to derive sur-face temperature. The atmospheric correctionand surface emissivity affect the derivation ofsurface temperature; hence, the uncertaintyis associated with the satellite measurement.

The surface temperature problem can becorrected using two methods, namely, directand indirect methods, where the direct methoduses the combination of atmospheric soundingand radiative transfer model but the indirectmethods only use the satellite observations.The along track scanning radiometer (ATSR)observation can improve the estimation byperforming the two nearly simultaneous mea-surements of brightness temperature from twodifferent view angles. The consideration of boththe directional radiometric surface tempera-ture and emissivity on high spectral resolution(Norman et al. 1995) can reduce the uncer-tainty to some limit.

(2) Uncertainties due to coverage problem ofsatellite data: Different spatial and temporalscale SEB components are needed for sev-eral relevant departments at global and localscales. The simultaneous acquiring of highspatial and temporal resolution imagery isvery hard because the satellites with highspatial coverage possess lower temporal fre-quency and vice versa. Also, the cloud cov-ers obscure entire or parts of scene in animage, making it nearly impossible to obtaincontinuous coverage of an area. Hence, thespatio-temporal coverage problem may renderthe satellite estimation method impractical inrelevant applications. There are some gap fill-ing procedures (Anderson et al. 2007) and cou-pling models (Renzullo et al. 2008) to resolvethis issue.

(3) Uncertainties in net radiation estimation: Netradiation is the key parameter of SEB, whichquantifies the available energy (Rn − G). How-ever, the net radiation estimation may lead toerrors due to the ignorance of diurnal varia-tion and phase difference between the diurnalcycles of each individual component (shortand longwaves). In most of the SEB methods,total Rn flux is considered without the rela-tive functions of direct and diffuse radiation.It is necessary to consider the effects of diffuseradiation than only direct radiation (Rodericket al. 2001).

(4) Uncertainties due to surface heterogeneity: Thesatellite measurement of some land surfacevariables such as temperature, aerodynamicresistance, leaf area index, fractional vegeta-tion coverage, plant height, etc. are highlysensitive to surface types. The observationalangular effect is prominent over homogeneous

J. Earth Syst. Sci. (2019) 128:84 Page 15 of 22 84

Table

4.Summary

ofthesatellitebasedevapotranspiration(latentheatflux)

estimationmodels(surface

energy

balance

based).

Nam

eofth

em

odel

sand

refe

rence

sM

ain

conce

pts

Adva

nta

ges

Dis

adva

nta

ges

Rec

om

men

dati

ons

Surf

ace

ener

gy

bala

nce

index

(SE

BI)

(Choudhury

and

Men

enti

1993)

Base

don

the

crop

wate

r

stre

ssin

dex

(CW

SI)

by

scaling

up

the

max

(dry

condit

ion)

and

min

(wet

condit

ion)

tem

per

atu

re

Dir

ect

effec

tsofsu

rface

tem

per

atu

reand

resi

stance

on

late

nt

hea

tflux

Poor

acc

ura

cy

Gro

und

base

dm

easu

rem

ent

isre

quir

ed

Inth

ism

odel

,it

isre

com

men

ded

to

use

ofair

pote

nti

alte

mper

atu

re

at

the

top

ofth

eA

tmosp

her

ic

Boundary

Lay

er(A

BL)

inst

ead

ofnea

rsu

rface

tem

per

atu

re

Sim

plified

SE

BI

(S-S

EB

I)

(Roer

inket

al.

2000;

Ver

stra

eten

etal.

2005)

The

obse

rvati

on

of

tem

per

atu

reis

alb

edo

dep

enden

tto

det

erm

ine

the

max

(dry

condit

ion)

and

min

(wet

condit

ion)

Gro

und

base

dm

easu

rem

ent

isnot

requir

ed

Extr

eme

tem

per

atu

res

are

loca

tion

dep

enden

t

The

des

ired

RS

image

should

conta

inth

eex

trem

eva

lues

ofsu

rface

tem

per

atu

re

Surf

ace

ener

gy

bala

nce

alg

ori

thm

for

land

(SE

BA

L)

(Bast

iaanss

en

2000;B

ast

iaanss

enet

al.

2005,

2010)

Am

oder

ate

appro

ach

base

d

on

both

the

empir

ical

rela

tionsh

ipand

para

met

eriz

ati

on

schem

e

Req

uir

esm

inim

um

gro

und

base

d

wea

ther

data

Auto

mati

cin

tern

alco

rrec

tion

of

atm

osp

her

iceff

ects

on

surf

ace

tem

per

atu

re

The

use

rdep

enden

t

spec

ifica

tion

ofanch

or

pix

els

The

SE

BA

Lis

reco

mm

ended

to

use

under

sever

alcl

imati

c

condit

ions

at

both

fiel

dand

catc

hm

ent

scale

sfo

rso

lvin

gw

ate

r

reso

urc

esand

irri

gati

on

pro

ble

ms

Surf

ace

ener

gy

bala

nce

syst

em(S

EB

S)

(Su

2002;

Maet

al.

2013;C

hen

etal.

2013;A

maty

aet

al.

2015)

Est

imate

the

act

ualE

Tand

oth

ersu

rface

fluxes

in

term

sofev

apora

tive

fract

ion

and

atm

osp

her

ic

turb

ule

nt

fluxes

Good

acc

ura

cy

The

roughnes

shei

ght

for

hea

t

transf

erca

nbe

calc

ula

ted

inst

ead

ofco

nst

ant

valu

e

Use

rfr

iendly

wit

hR

Sand

GIS

soft

ware

The

unce

rtain

ties

can

be

part

ially

solv

ed

Req

uir

esm

ore

para

met

ers

The

solu

tion

oftu

rbule

nt

flux

isre

lati

vel

yco

mple

x

This

alg

ori

thm

isre

com

men

ded

for

som

esp

ecia

lir

rigati

on

are

alike

Cole

am

bally

irri

gati

on

are

a(C

IA)

and

als

oth

eto

pogra

phic

enhance

dSE

BS

(TE

SE

BS)

is

sugges

ted

for

com

ple

xte

rrain

are

as

Mappin

gev

apotr

ansp

irati

on

at

hig

hre

solu

tion

wit

h

inte

rnalize

dca

libra

tion

(ME

TR

IC)

(Allen

etal.

2013;C

arr

illo

-Roja

set

al.

2016)

Exte

nded

from

SE

BA

Lw

ith

consi

der

ing

slope

asp

ect

Slo

pe

asp

ect

isco

nsi

der

edU

nce

rtain

ties

found

inth

e

det

erm

inati

on

ofanch

or

pix

els

This

alg

ori

thm

ishig

hly

reco

mm

ended

for

hig

her

reso

luti

on

images

Tw

oso

urc

em

odel

(TSM

)

(Liet

al.

2005;Y

anget

al.

2015;Sun

2016)

Itdiv

ides

the

com

posi

te

radio

met

ric

tem

per

atu

res

into

two

sourc

es–

one

isso

il

and

anoth

eris

veg

etati

ve

canopy

then

sum

-up

the

sensi

ble

hea

tfluxes

for

each

The

vie

wgeo

met

ryis

consi

der

ed

Em

pir

icalco

rrec

tions

are

not

requir

ed

Too

many

gro

und

mea

sure

men

tsare

requir

ed

Tw

oobse

rvati

on

per

iods

are

reco

mm

ended

toper

form

the

separa

tem

easu

rem

ent

ofsu

rface

tem

per

atu

re

84 Page 16 of 22 J. Earth Syst. Sci. (2019) 128:84

and dense vegetated surfaces but troublesomeover heterogeneous surfaces (Carlson et al.1994; Norman et al. 1995).

(5) Inconsistency in satellite estimation models:Different models are useful for different landsurface types and meteorological conditions.Till date, there is no universal model, whichcould be used throughout the world. So, weneed the modifications/improvements of themodel to estimate SEB components at globalscale, which leads to uncertainties.

(6) Insufficient near surface meteorological andflux data: Most of the satellite-based estimationmodels need the near surface meteorologicaldata. Basically, the data from meteorologi-cal stations are obtained at a satellite pixelby spatial interpolation techniques. Differentstudy regions have different climatic and ter-rain conditions with sparse/irregular meteoro-logical and surface flux measurement stations.Therefore, the accuracy of the interpolationmethods should be improved, as well as theground-based meteorological and flux measure-ment networks also need further development.

(7) Night-time transpiration and early morningdew: If night-time transpiration occurs over ahighly vegetated surface and this may be a sig-nificant error source in satellite estimation dueto the nocturnal vapour pressure difference andwind speed (Dawson et al. 2007). Early morn-ing dew over well-irrigated vegetation surfacemay affect the satellite measured radiant tem-perature (Pinter 1986). Hence, we should thinkabout these issues before obtaining the satelliteimagery.

In addition to the above-mentioned issues, otheruncertainties in satellite measurements such aslimitations of empirical vegetation index mod-els, spatio-temporal scaling effects, lack of SEBcomponents at satellite pixel for truth valida-tion, etc. have been discussed in the literature(Wang et al. 2007; Kalma et al. 2008; Li et al.2009).

6. Recommendations

In this study, we have discussed the advancements,limitations and uncertainties associated withdifferent ground and satellite-based estimationmethods and models and also provided some rec-ommendations to researchers so that they can usethese methods more specifically. The summarised

recommendations, as indicated in tables 2–4, canbe explained in brief as follows to specify the keypoints for suitable applications of the respectivemethods and models:

(1) Recommendations on solar radiation estima-tion methods: Estimation of solar radiationat a large scale has many uses in the Earthsystem and photovoltaic power system appli-cations. There are three categories of meth-ods to estimate solar radiation. In the LUTmethod, a large number of radiative trans-fer model (RTM) calculations (105–107) arerequired if specified scientific approaches arenot applied (Mueller et al. 2009), where eigen-vector approach is useful to reduce the RTMcalculations by several orders. So, the useof a scientific approach such as eigenvectorapproach is recommended for the RTM-basedmethods. The parametrisation scheme is imple-mented with MODIS data product needs foran extensive error analysis to find out themajor error sources of the model (Wang andPinker 2009). Hence, an extensive error analy-sis is needed for parameterisation scheme withmoderate resolution images. The geostationarysatellite with high temporal frequency such asmulti-functional transport satellite (MTSAT)is more suitable for continuous estimation ofsolar radiation using the statistical method(Lu et al. 2011). For continuous estimationof solar radiation, the ANN-based statisticalapproaches are recommended using time-seriesimages.

(2) Recommendations on thermal radiation esti-mation methods: Thermal (longwave) radiationis important for the radiative cooling process(Kiehl and Trenberth 1997) to balance theabsorption of solar radiation. Here, we compilesome recommendations on three major cate-gories of estimation methods. The empiricalmethod that combines the uses of satellite ther-mal data and atmospheric parameters is notperfect in extreme climate conditions (Yu et al.2014). Hence, the re-training of algorithm isrecommended where the empirical method usesboth thermal and atmospheric parameters. Ifthe RTM uses the common calculation of allskies, the model performance degrades (Zhouet al. 2007). Therefore, separate calculationfor clear and cloudy sky is suggested. In thecase of hybrid method, some statistical algo-rithms frequently overestimate the longwave

J. Earth Syst. Sci. (2019) 128:84 Page 17 of 22 84

radiation over arid or desert surfaces wherethe ground-air temperature is high. Yu et al.(2013) used a correction method and foundthat the root means square error (RMSE)was substantially reduced. Therefore, a correc-tion method is needed for model coefficientsderivation from the ground-air temperaturedifference to reduce the overestimation of long-wave radiation.

(3) Recommendations on ET estimation methods:ET is a vitally important component ofterrestrial energy, water and bio-geophysicalcycle. We make some important recommen-dations on various SEB-based ET estima-tion methods. The SEBI model is the surfacetemperature-based parametrisation scheme toestimate the location-dependent ET, where theuse of air temperature at the top of atmo-spheric boundary layer is recommended insteadof near surface temperature (Choudhury andMenenti 1993). Simplified SEBI (S-SEBI) is themaximum and minimum temperature-basedestimation method, where no additional meteo-rological data are needed if the surface extremes(max and min of surface temperature) areavailable (Roerink et al. 2000). Hence, thedesired satellite image should contain theextreme value of surface temperature. TheSEBAL model is an iterative and feedback-based numerical procedure that estimates sur-face fluxes using both the satellite and grounddata. This model is widely accepted and rec-ommended to use under several climatic con-ditions at both field and catchment scales forsolving water resources and irrigation prob-lems (Bastiaanssen et al. 2005). In SEBS,surface fluxes are estimated from satellite andground data in terms of EF. This model isrecommended to estimate ET for some specialirrigation area such as Coleambally irrigationarea (CIA) (Ma et al. 2013). The modifiedSEBS such as topographic enhanced SEBS(TESEBS) is suggested for areas with com-plex terrain (Chen et al. 2013; Amatya et al.2015). The METRIC is an extension of SEBALversion with consideration of the slope aspectand is used for complex terrain areas withhigher resolution satellite data (Carrillo-Rojaset al. 2016). This method is recommendedfor longer and higher mountainous areas withhigher resolution satellite data. TSM modeldivides the composite radiometric tempera-ture into two sources (soil and canopy), where

overestimation occurs due to the uncertaintiesthat arise from the determination of PT coef-ficients and iteration procedure (Yang et al.2015). Here, the careful selection of target cri-teria is suggested for iteration process, and twoobservation periods are also recommended toperform the separate measurement of surfacetemperature.

However, the above complied recommendationscan be applied properly on the following consi-derations: estimation manner (instantaneous/continuous); study area’s characteristics (landsurface types, climate conditions); availability ofsatellite and ground data (spatial and temporalresolution, access criteria), etc.

7. Conclusions and perspectives

This paper reviews previous and recent studies onthe estimation methods of the Earth’s SEB com-ponents from ground and satellite measurements.We summarise the main scientific concepts, merits,demerits, errors and uncertainties of the studiedmethods and models and also provide some impor-tant recommendations to researchers on how tomake use of these methods. In a broad sense, therehas been a firm progress but this research area stillfaces many challenges.

The ground-based measurement instrumentssuch as pyranometer, pyrgeometer, lysimeter, ECsystem and scintillometer have become moreefficient and user friendly due to the rapid develop-ments in electronics and communication tech-nology. Therefore, the errors and uncertaintiesassociated with ground measurements are negligi-ble. But due to the limitation and lack of properregional and global coverage, the worldwide groundmeasurement networks are not self-disciplined andunified. In the last three decades, satellite remotesensing technologies have developed significantlyand the wide availability of satellite data productshas enabled researchers to develop a wide spectrumof satellite-based estimation methods and models.

From this review work, we have observed thateach method and model has its own advantages anddisadvantages relative to other approaches, andthere is no consensus on which one is the best. Inreality, these are the important tools for estimatingthe SEB components at regional and global scales.There are several methods for satellite estimationof solar and thermal radiation. The RTM has astrong validity of physics (i.e., the RTM model

84 Page 18 of 22 J. Earth Syst. Sci. (2019) 128:84

follows the basic theory of radiation physics) andcan be applied to all atmospheric and land surfaceprofiles. Among other methods and parameterisa-tion schemes, the use of hybrid method may achievea better generalisation, which is highly expectedfor universal applications. Most of the SEB-basedmodels are estimating latent heat or sensible heatfluxes as the residual of SEB by using satellitedata and some additional ground-based meteoro-logical data. No additional data are needed in theS-SEBI model if the surface extremes (max andmin surface temperatures) are present in the satel-lite imagery. In SEBAL, it is required to determinea constant temperature for dry and wet condi-tions because the extreme temperatures vary withreflectance changes as a consequence of the dry andwet conditions. It has some important advantagessuch as minimum ground-based data and auto-matic internal calibration within each processedimage. The SEBS estimates H and LE distinctivelyunder dry and wet limits in terms of EF for everypixel.

However, the accuracy of surface flux estima-tion using these methods varies from one modelto another, one study area to another and onestudy period to another. Su et al. (2005) reportedthe accuracy of ET value estimated from SEBSwas 10–15% with respect to ground-based measure-ment, where the EF ranged from 0.5 to 0.9. A max-imum relative difference of 8% between measuredand estimated EF was observed in the S-SEBImodel (Roerink et al. 2000). The typical accuracyof SEBAL was tested under several climatic con-ditions at field scale and it was found to be 85%and 95% at daily and seasonal scales, respectively(Bastiaanssen 2000; Bastiaanssen et al. 2005). TheSEBAL and SEBS have some limitations overmountainous area (Bastiaanssen et al. 2010; Chenet al. 2013). These limitations can be solved usingMETRIC and TESEBS models as they considerthe slope aspect (Allen et al. 2007; Amatya et al.2015). The TSM method is used for separate cal-culation of soil and canopy heat fluxes to improvethe accuracy (Norman et al. 1995). Along withother uncertainties as described in the earlier sec-tion, uncertainties associated with the validationof satellite retrieved radiation quantities with theground measurement are common in all satelliteestimations. To overcome these uncertainties, thecross calibration within the same measurement net-work and among the different networks as wellas the consistent processing and effective manage-ment of ground measurements is needed. Another

difficulty is in the inter-comparison of the errorcalculations between ground and satellite estima-tion as they use different error measuring variablesused in different studies such as bias, mean bias,mean absolute error, RMSE, percentage error,standard deviation, etc.

Although the reviewed methods and modelsdemonstrate an enough capability for surface fluxestimations, but still have some limitations whichlead to errors and uncertainties. Therefore, futureresearch can be focused on several directions.Newly developed methods in acquisition of satelliteand ground data are needed to solve the addresseduncertainties and limitations. Hybrid methods orintegration of some methods can be used to takethe advantage of their respective merits and com-pensating for their limitations. The use of datafusion and data assimilation techniques can behighly useful for integrated estimations. The satel-lite estimation methods also have a large area tobe improved for using the recent high-resolutionsatellite data as relevant satellite data are rapidlygrowing.

Acknowledgements

This study was financially supported by theNational Key Research and Development Pro-gram of China (grant nos. 2016YFA0602302 and2016YFB0502502). We also wish to acknowledgethe intellectual and material contributions of CAS-TWAS President’s Fellowship.

References

Allen R, Tasumi M and Trezza R 2007 Satellite-based energybalance for mapping evapotranspiration with internalizedcalibration (METRIC)-model; J. Irrig. Drain. Eng. 133380–394.

Allen R, Burnett B, Kramber W H, Kjaersgaard J, KilicA, Kelly C and Trezza R 2013 Automated calibration ofthe METRIC-landsat evapotranspiration process; J. Am.Water Resour. Assoc. 49 563–576.

Amatya P, Ma Y, Han C, Wang B and Devkota L 2015 Map-ping regional distribution of land surface heat fluxes onthe southern side of the central Himalayas using TESEBS;Theor. Appl. Climatol. 124 835–846.

Anderson M C, Norman J M, Mecikalski J R, Otkin J A andKustas W P 2007 A climatological study of evapotranspi-ration and moisture stress across the continental UnitedStates based on thermal remote sensing: 1. Model formula-tion; J. Geophys. Res. Atmos. 112 D10117:1–D10117:17.

ASCE–EWRI 2005 The ASCE standardized reference evap-otranspiration equation; ASCE–EWRI Standardization of

J. Earth Syst. Sci. (2019) 128:84 Page 19 of 22 84

Reference Evapotranspiration Task Committee Report,ASCE Reston, VA.

Augustine J, Hodges G, Cornwall C, Michalsky J and MedinaC 2005 An update on SURFRAD – The GCOS sur-face radiation budget network for the continental UnitedStates; J. Atmos. Oceanic Technol. 22 1460–1472.

Baldocchi D, Falge E, Gu L, Olson R, Hollinger D, RunningS, Anthoni A, Bernhofer C, Davis K, Evans R, Fuentes J,Goldstein A, Katul G, Law B, Lee X H, Malhi Y, MeyersT, Munger W, Oechel W, Pilegaard K and Wofsy S 2001A new tool to study the temporal and spatial variability ofecosystem-scale carbon dioxide, water vapor, and energyflux densities; Bull. Am. Meteor. Soc. 82 2415–2434.

Barkstrom B R and Smith G L 1986 The earth radia-tion budget experiment: Science and implementation; Rev.Geophys. 24 379–390.

Baseline surface radiation network (n.d.) http://www.bsrn.awi.de/

Bastiaanssen W 1995 Regionalization of surface flux den-sities and moisture indicators in composite terrain; PhDThesis, Wageningen Agricultural University, Wageningen,The Netherlands.

Bastiaanssen W 2000 SEBAL-based sensible and latent heatfluxes in the irrigated Gediz Basin Turkey; J. Hydrol. 22987–100.

Bastiaanssen W, Menenti M, Feddes R and Holtslag A 1998aA remote sensing surface energy balance algorithm forland (SEBAL): 1. Formulation; J. Hydrol. 212–213 198–212.

Bastiaanssen W, Pelgrum H, Wang J, Ma Y, Moreno J,Roerink G and van der Wal T 1998b A remote sensingsurface energy balance algorithm for land (SEBAL): 2.Validation; J. Hydrol. 212–213 213–229.

Bastiaanssen W, Noordman E, Pelgrum H, Davids G, Thore-son B and Allen R 2005 SEBAL model with remotelysensed data to improve water-resources managementunder actual field conditions; J. Irrig. Drain. Eng. 13185–93.

Bastiaanssen W, Thoreson B, Clark B and Davids G 2010Discussion of application of SEBAL model for mappingevapotranspiration and estimating surface energy fluxes inSouth-Central Nebraska by Ramesh K Singh, Ayse Irmak,Suat Irmak and Derrel L Martin; J. Irrig. Drain. Eng. 136282–283.

Bonan G B 2008 Ecological Climatology: Concepts and Appli-cation; 2nd edn, Cambridge University Press, Cambridge,Chapter 1, pp. 1–24.

Bowen I S 1926 The ratio of heat losses by conduction andevaporation from any water surface; Phys. Rev. 27 779–787.

Carlson T N, Gillies R R and Perry E M 1994 A methodto make use of thermal infrared temperature and NDVImeasurements to infer surface soil water content andfractional vegetation cover; Remote Sens. Rev. 9 161–173.

Carrillo-Rojas G, Silva B, Cordova M, Celleri R and BendixJ 2016 Dynamic mapping of evapotranspiration usingan energy balance-based model over an Andean ParamoCatchment of Southern Ecuador; Remote. Sens. (Basel) 8160.

Chen X, Su Z, Ma Y, Yang K and Wang B 2013 Estima-tion of surface energy fluxes under complex terrain of

Mt. Qomolangma over the Tibetan Plateau; Hydrol. EarthSyst. Sci. 7 1607–1618.

Choudhury B and Menenti M 1993 Parameterization ofland surface evaporation by means of location depen-dent potential evaporation and surface temperature range;Department for Environment, Food and Rural Affairs(Defra), London, UK, Vol. 212, pp. 561–568.

Cros S and Wald L 2003 Survey of the main databases pro-viding solar radiation data at ground level; In: Proceedingsof the 23rd EARSeL annual symposium remote sensing intransition (ed.) Goossens R I and Ghent, Belgium, pp.491–497.

Dawson T E, Burgess S S O, Tu K P, Oliveira R S, SantiagoL S and Fisher J B 2007 Nighttime transpiration in woodyplants from contrasting ecosystems; Tree Physiol. 27 561–575.

Diak G R, Mecikalski J R, Anderson M C, Norman J M,Kustas W P, Torn R D and Dewolf R L 2004 Estimat-ing land surface energy budgets from space: Review andcurrent efforts at the university review and current effortsat the University of Wisconsin-Madison and USDA-ARS;Bull. Am. Meteor. Soc. 85(1) 65–76.

Dutta D, Mahalakshmi D, Singh M, Goyal P, Paul S, SharmaJ and Dadhwal V 2015 Satellite-Based estimation ofinstantaneous radiative fluxes over continental USA – Acase study; J. Indian Soc. Remote Sens. 43(4) 1–9.

Ellingson R, Ferraro R and Gruber A 1983 An examinationof a technique for estimating the longwave radiation bud-get from satellite radiance observations; Adv. Space Res. 221–23.

Fisher J, Tu K and Baldocchi D 2008 Global estimates of theland-atmosphere water flux based on monthly AVHRRand ISLSCP-II data, validated at 16 FLUXNET sites;Remote Sens. Environ. 112 901–919.

FLUXNET A Global Network (n.d.) https://fluxnet.ornl.gov/

Foken T 2008 The energy balance closure problem: Anoverview; Ecol. Appl. 18 1351–1367.

Gavilan P and Berengena J 2007 Accuracy of the Bowenratio-energy balance method for measuring latent heatflux in a semiarid advective environment; IrrigationSci. 25 127–140.

Gebler S, Hendricks Franssen H-J, Putz T, Post H, SchmidtM and Vereecken H 2015 Actual evapotranspiration andprecipitation measured by lysimeters: A comparison witheddy covariance and tipping bucket; Hydrol. Earth Syst.Sci. 19 2145–2216.

Gilgen H and Ohmura A 1999 The global energy balancearchive; Bull. Am. Meteor. Soc. 80 831–850.

Global Energy and Water Cycle Exchange (n.d.) http://www.gewex.org/

Guide to Meteorological Instruments and Methods of Obser-vation (7th edn) 2008 https://www.wmo.int/pages/prog/

gcos/documents/gruanmanuals/CIMO/CIMO Guide-7th

Edition-2008.pdf

Ha W, Kolb T, Springer A, Dore S, O’Donnell F, MoralesR, Lopez S M and Koch G 2015 Evapotranspirationcomparisons between eddy covariance measurements andmeteorological and remote-sensing-based models in dis-turbed ponderosa pine forests; Ecohydrology 8 1335–1350.

Harries J E, Russell J E, Hanafin J A, Brindley H, FutyanJ, Rufus J, Kellock S, Matthews G, Wrigley R, Last A,

84 Page 20 of 22 J. Earth Syst. Sci. (2019) 128:84

Mueller J, Mossavati R, Ashmall J, Sawyer E, Parker D,Caldwell M, Allan R P, Smith A, Bates M J and CoanB 2005 The geostationary earth radiation budget project;Bull. Am. Meteor. Soc. 83 977–992.

Hartmann D 1994 Global Physical Climatology ; InternationalGeophysics Series Academic Press, London, UK, 56p.

Hena M, Ali M and Rahman M 2013 A simple statisticalmodel to estimate incident solar radiation at the surfacefrom NOAA AVHRR satellite data; Int. J. Inf. Technol.Comput. Sci. 02 36–41.

Huang G, Ma M, Liang S, Liu S and Li X 2011 A LUT basedapproach to estimate surface solar irradiance by com-bining MODIS and MTSAT data; J. Geophys. Res. 116D22201:1–D22201:14.

Jackson R, Idso S and Reginato R P 1981 Canopy tem-perature as a crop water stress indicator; Water Resour.Res. 17 1133–1138.

Jacobowitz H and Tighe R 1984 The earth radiation budgetderived from the Nimbus-7 ERB experiment; J. Geophys.Res. 89 4997–5010.

Jiao Z, Yan G, Zhao J, Wang T and Chen L 2015 Estima-tion of surface upward longwave radiation from MODISand VIIRS clear-sky data in the Tibetan Plateau; RemoteSens. Environ. 162 221–237.

Kalma J D, McVicar T R and McCabe M F 2008 Esti-mating land surface evaporation: A review of methodsusing remotely sensed surface temperature data; Surv.Geophys. 29 421–469.

Kawai Y and Kawamura H 2005 Validation and improve-ment of satellite derived surface solar radiation over thenorthwestern Pacific Ocean; J. Oceanogr. 61 79–89.

Kiehl J T and Trenberth K E 1997 Earth’s annual globalmean energy budge; Bull. Am. Meteor. Soc. 78 197–208.

Kim D and Ramanathan V 2008 Solar radiation budget andradiative forcing due to aerosols and clouds; J. Geophys.Res. 113 D02203:1–D02203:34.

Krishnamurti T N and Biswas M K 2006 Transitions in thesurface energy balance during the life cycle of a monsoonseason; J. Earth Syst. Sci. 115(2) 185–201.

Kustas W 1990 Estimates of evapotranspiration with aone-layer and 2-layer model of heat-transfer over partialcanopy cover; J. Appl. Meteorol. 29 704–715.

Kustas W and Norman J 1999 Evaluation of soil and veg-etation heat flux predictions using a simple two-sourcemodel with radiometric temperatures for partial canopycover; Agric. Forest. Meteorol. 94 13–29.

L’ecuyer T S, Beaudoing H K, Rodell M, Olson W, LinB, Kato S, Clayson C A, Wood E, Sheffield J, Adler R,Huffman G, Bosilovich M, Gu G, Robertson F, Houser PR, Chambers D, Famiglietti J S, Fetzer E and Liu W T2015 The observed state of the energy budget in the earlytwenty-first century; J. Clim. 28 8319–8346.

Lee M-I, Kang I-S and Kim J-K 2001 Influence of cloud-radiation interaction on simulating tropical intraseasonaloscillation with an atmospheric general circulation model;J. Geophys. Res. 106 14,219–14,233.

Li F, Kustas W, Prueger J, Neale C and Jackson T 2005Utility of remote sensing based two-source energy balancemodel under low and high vegetation cover conditions;J. Hydrometeorol. 6 878–891.

Li Z, Tang R, Wan Z, Bi Y, Zhou C, Tang B, Yan Gand Zhang X 2009 A review of current methodologies

for regional evapotranspiration estimation from remotelysensed data; Sensors 9 3801–3853.

Liang S, Zheng T, Liu R G, Fang H L, Tsay S C and RunningS 2006 Estimation of incident photosynthetically activeradiation from moderate resolution imaging spectrometerdata; J. Geophys. Res. 111 D15208:1–D15208:13.

Liang S, Wang K and Wild X Z 2010 Review on estima-tion of land surface radiation and energy budgets fromground measurements, remote sensing and model simula-tions; IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 3225–240.

Lichun P, Wanbiao L, Jing Y, Dong C, Yuming L and Lijia C2015 A review of parameterization methods for downwardshortwave and longwave radiation on the surface; ActaSci. Nat. Univ. Pekin. 51 772–782.

Liou Y-A and Kar S 2014 Evapotranspiration estimationwith remote sensing and various surface energy balancealgorithms – A review; Energies 7 2821–2849.

Liu Y, Hiyama T, Yasunari T and Tanaka H 2012 A non-parametric approach to estimating terrestrial evaporation:Validation in eddy covariance sites; Agric. Forest. Meteo-rol. 157 49–59.

Long C and Dutton E G 2002 BSRN Global Network rec-ommended QC tests, V2.0; http://hdl.handle.net/10013/epic.38770.d001

Lu N, Liu R, Liu J and Liang S 2010 An algorithm for esti-mating downward shortwave radiation from GMS 5 visibleimagery and its evaluation over China; J. Geophys. Res.Atmos. 115 D18102:1–D18102:15.

Lu N, Qin J, Yang K and Sun J 2011 A simple and efficientalgorithm to estimate daily global solar radiation fromgeostationary satellite data; Energy 36 3179–3188.

Ma Y and Pinker R T 2012 Modeling shortwave radiativefluxes from satellites; J. Geophys. Res. 117 D23202:1–D23202:19.

Ma W, Hafeez M, Ishikawa H and Ma Y 2013 Evaluation ofSEBS for estimation of actual evapotranspiration usingASTER satellite data for irrigation areas of Australia;Theor. Appl. Climatol. 112 609–616.

Main Geophysical Observatory, World Radiation Data Cen-ter, St. Petersburg, Russia, http://wrdc.mgo.rssi.ru

Meijninger W 2003 Surface fluxes over natural landscapesusing scintillometry; PhD Thesis, Wageningen University,Wageningen, The Netherlands.

MODIS https://terra.nasa.gov/about/terra-instruments/modis

Mueller R, Matsoukas C, Gratzki A and Hollmann R 2009The CM–SAF operational scheme for the satellite basedretrieval of solar surface irradiance – A LUT basedeigenvector hybrid approach; Remote Sens. Environ. 1131012–1024.

Nieveen J and Green A 1998 Measuring sensible heat fluxover pasture using the Ct2 profile method; Bound. LayerMeteorol. 91 23–35.

Norman J, Kustas W and Humes K 1995 Source approachfor estimating soil and vegetation energy fluxes in obser-vations of directional radiometric surface temperature;Agric. Forest. Meteorol. 77 263–293.

Nouri H, Beecham S, Kazemi F and Hassanli A 2013 Areview of ET measurement techniques for estimating thewater requirements of urban landscape vegetation; UrbanWater J. 10 247–259.

J. Earth Syst. Sci. (2019) 128:84 Page 21 of 22 84

Ohmura A, Dutton E G, Forgan B, Frohlich C, Gilgen,H, Hegner H, Heimo A, Konig-Langlo B, McArthur B,Muller G, Philipona R, Pinker R, Whitlock C H, DehneK and Wild M 1998 Baseline surface radiation network(BSRN/WCRP): New precision radiometry for climateresearch; Bull. Am. Meteor. Soc. 79 2115–2136.

Pan X, Liu Y and Fan X 2016 Satellite retrieval of surfaceevapotranspiration with nonparametric approach: Accu-racy assessment over a semiarid region; Adv. Meteorol.2016, ID 1584316:1–ID 1584316:14.

Park M-S, Ho C-H, Cho H and Choi Y-S 2015 Retrievalof outgoing longwave radiation from COMS narrowbandinfrared imagery; Adv. Atmos. Sci. 32 375–388.

Paulescu M, Paulescu E, Gravila P and Badescu V 2013Weather modeling and forecasting of PV systems oper-ation; Springer-Verlag, London, Vol. XVIII, Chapter 2,pp. 20–24.

Pauwels V and Samson R 2006 Comparison of different meth-ods to measure and model actual evapotranspiration ratesfor a wet sloping grassland; Agric. Water Manag. 82 1–24.

Pinter P J Jr 1986 Effect of dew on canopy reflectance andtemperature; Remote Sens. Environ. 19 187–205.

Pyrgeometer (n.d.) https://en.wikipedia.org/wiki/Pyrgeometer

Renzullo L J, Barrett D J, Marks A S, Hill M J, Guer-schman J P and Mu Q 2008 Multi-sensor model-datafusion for estimation of hydrologic and energy flux param-eters; Remote Sens. Environ. 112 1306–1319.

Rigollier C, Lefevre M and Wald L 2004 The methodHeliosat-2 for deriving shortwave solar radiation fromsatellite images; Sol. Energy 77 159–169.

Roderick M L, Farquhar G D, Berry S L and Noble I R 2001On the direct effect of clouds and atmospheric particleson the productivity and structure of vegetation; Oecolo-gia 129 21–30.

Roerink G, Su Z and Menenti M 2000 S-SEBI: A simpleremote sensing algorithm to estimate the surface energybalance; Phys. Chem. Earth B 25 147–157.

Ryu Y, Baldocchi D D, Kobayashi H, Ingen C V, Li J, BlackT A, Beringer J, Gorsel E V, Knohl A, Law B E and Roup-sard O 2011 Integration of MODIS land and atmosphereproducts with a coupled-process model to estimate grossprimary productivity and evapotranspiratiom from 1 kmto global scale; Global Biogeochem. Cycles 25 GB4017:1–GB4017:24.

Samain B, Simons G, Voogt M, Defloor W, Bink N-J andPauwels V 2012 Consistency between hydrological model,large aperture scintillometer and remote sensing basedevapotranspiration estimates for a heterogeneous catch-ment; Hydrol. Earth Syst. Sci. 16 2095–2107.

Sanchez J, Kustas W, Caselles V and Anderson M 2007 Mod-elling surface energy fluxes over maize using a two-sourcepatch model and radiometric soil and canopy temperatureobservations; Remote Sens. Environ. 112 1130–1143.

Schmetz J 1989 Towards a surface radiation climatology:Retrieval of downward irradiances from satellites; Atmos.Res. 23 287–321.

Schmetz J, Pili P, Tjemkes S, Just D, Kerkmann J, Rota Sand Ratier A 2002 An introduction to Meteosat SecondGeneration (MSG); Bull. Am. Meteor. Soc. 83 977–992.

Schmithusen H, Sieger R and Konig-Langlo G 2012 BSRNtoolbox – A tool to create quality checked output files

from BSRN datasets and station-to-archive files; AlfredWegener Institute, Helmholtz Centre for Polar and MarineResearch, Bremerhaven.

Schumacher C, Houze Jr R and Kraucunas I 2004 The tropi-cal dynamical response to latent heating estimates derivedfrom the TRMM precipitation radar; J. Atmos. Sci. 611341–1358.

Shang-Ping Xie, Kosaka Y and Okumura Y M 2016 Dis-tinct energy budgets for anthropogenic and naturalchanges during global warming hiatus; Nat. Geosci. 9 29–33.

Shi T, Guan D, Wu J, Wang A, Jin C and Han S 2015Comparison of methods for estimating evapotranspirationrate of dry forest canopy: Eddy covariance, Bowen ratioenergy balance, and Penman-Monteith equation; J. Geo-phys. Res.: Atmos. 19 2145–2161.

Slingo A and Slingo J 1988 The response of general circula-tion model to cloud longwave radiative forcing. I: Intro-duction and initial experiments; Quart. J. Roy. Meteorol.Soc. 114 1027–1062.

Solar Instruments/Atmospheric Science Instruments,http://www.kippzonen.com/

Soumi NPP, https://www.nasa.gov/mission pages/NPP/main/index.html

Stephens G L and L’Ecuyer T 2013 The global energybalance from a surface prospective; Clim. Dyn. 40 3107–3134.

Su Z 2002 The surface energy balance system (SEBS) forestimation of turbulent heat fluxes; Hydrol. Earth Syst.Sci. 6 85–99.

Su Z, Li X, Zhou Y, Wan L, Wen J and Sintonen K 2003Estimating areal evaporation from remote sensing; Proc.IEEE Int. 2 1166–1168.

Su H, Mccabe M F, Wood E F, Su Z and Prueger J H 2005Modeling evapotranspiration during SMACEX: Compar-ing two approaches for local- and regional-scale prediction;J. Hydrometeorol. 6 910–922.

Sun H A 2016 Two-source model for estimating evaporativefraction (TMEF) coupling Priestley–Taylor formula andtwo-stage trapezoid; Remote Sens. 8 248.

Sun Z, Liu J, Zeng X and Liang H 2012 Parameterizationof instantaneous global horizontal irradiance: Cloudy-skycomponent; J. Geophys. Res. 117 D14202:1–D14202:10.

Surface Radiation (SURFRAD) Network (n.d.) http://www.esrl.noaa.gov/gmd/grad/surfrad/

Tang Q, Peterson S, Cuenca R, Hagimoto Y and Letten-maier D 2009 Satellite-based near-real-time estimationof irrigated crop water consumption; J. Geophys. Res.Atmos. 114 D05114:1–D05114:14.

Tang W, Qin J, Yang K, Liu S, Lu N and Niu X 2016 Retriev-ing high-resolution surface solar radiation with cloudparameters derived by combining MODIS and MTSATdata; J. Geophys. Res. Atmos. 16 2543–2557.

The Advanced Space-borne Thermal Emission and Reflec-tion Radiometer, http://asterweb.jpl.nasa.gov/

The Clouds and the Earth’s Radiant Energy System, http://ceres.larc.nasa.gov/

The Geostationary Operational Environmental Satellite-Advanced Baseline Imager(ABI), http://www.goes-r.gov/spacesegment/abi.html

Trenberth K, Fasullo J and Kiehl J 2009 Earth’s globalenergy budget; Bull. Am. Meteor. Soc. 90 311–323.

84 Page 22 of 22 J. Earth Syst. Sci. (2019) 128:84

Vazquez-Navarro M, Mayer B and Mannstein H 2013 Afast method for the retrieval of integrated longwave andshortwave top-of-atmosphere upwelling irradiances fromMSG/SEVIRI (RRUMS); AMT 6 2627–2640.

Verstraete W, Veroustraete F and Feyen J 2005 Estimat-ing evapotranspiration of European forests from NOAA-imagery at satellite overpass time: Towards an operationalprocessing chain for integrated optical and thermal sensordata products; Remote Sens. Environ. 96 256–276.

Wan Z, Zhang K, Xue X, Hong Z, Hong Y and GourleyJ 2015 Water balance based actual evapotranspirationreconstruction from ground and satellite observations overthe Conterminous United States; Water Resour. Res. 516485–6499.

Wang J and Bras R 2011 A model of evapotranspirationbased on the theory of maximum entropy production;Water Resour. Res. 47 W03521:1–W03521:10.

Wang K and Liang S 2008 An improved method forestimating global evapotranspiration based on satellitedetermination of surface net radiation, vegetation index,temperature, and soil moisture; J. Hydrometeorol. 9 712–727.

Wang K and Liang S 2009 Global atmospheric downwardlongwave radiation over land surface under all-sky con-ditions from 1973 to 2008; J. Geophys. Res. Atmos. 114D19101:1–D19101:12.

Wang W and Liang S 2010 A method for estimating clear-skyinstantaneous land surface longwave radiation from GOESsounder and GOES-R ABI data; IEEE Geosci. RemoteSens. Lett. 7 708–712.

Wang H and Pinker R T 2009 Shortwave radiative fluxesfrom MODIS: Model development and implementation;J. Geophys. Res. 114 D20201:1–D20201:17.

Wang K, Wang P, Li Z, Cribb M and Sparrow M 2007A simple method to estimate actual evapotranspirationfrom a combination of net radiation, vegetation index,and temperature; J. Geophys. Res. Atmos. 112 D15107:1–D15107:14.

Wang P, Sneep M, Veefkind J, Stammes P and Levelt P 2014Evaluation of broadband surface solar irradiance from theozone monitoring instrument; Remote Sens. Environ. 14988–99.

Ward H and Evans J G 2015 Infrared and millimetre-wavescintillometry in the suburban environment – Part 2:Large-area sensible and latent heat fluxes; Atmos. Meas.Tech. 8 1407–1424.

Wild M, Folini D, Schar C, Loeb N, Dutton E and LangloG 2009 Earth global energy budget; Bull. Am. Meteor.Soc. 90 311–323.

World Climate Research Programme, http://www.wcrp-climate.org

Yan G, Wang T, Jiao Z, Mu X, Zhao J and Chen L 2016Topographic radiation modeling and spatial scaling ofclear-sky land surface longwave radiation over ruggedterrain; Remote Sens. Environ. 172 15–27.

Yang Y, Long D, Guan H, Liang W, Simmons C andBatelaan O 2015 Comparison of three dual-source remotesensing evapotranspiration models during the MUSOEXE-12 campaign: Revisit of model physics; WaterResour. Res. 51 3145–3165.

Yeom J and Han K 2010 Improved estimation of surface solarinsolation using a neural network and MTSAT-1R data;Comput. Geosci. 36 590–597.

Yingying C, Jiancheng S, Yuanyuan Q and Lingmei J2008 The simulation study on land surface energy budgetover China area based on Lis-Noah Land Surface Model ;ISPRS, Beijing, Vol. XXXVII.

Yu S, Xin X and Liu Q 2013 Estimation of clear-sky longwavedownward radiation from HJ-1B thermal data; Sci. China:Earth Sci. 56 829–842.

Yu S, Xin X and Zhang H 2014 Algorithms comparison forcalculating downward longwave radiation by MODIS dataunder clear and cloudy skies; In: Proc. SPIE 9242 924210.

Zelenka A, Perez R, Seals R and Renne D 1988 Effectiveaccuracy of the satellite-derived hourly irradiance; Theor.Appl. Climatol. 62 199–207.

Zhang K, Kimball J S, Mu Q, Jones L A, Goetz S J andRunning S W 2009 Satellite based analysis of northernET trends and associated changes in the regional waterbalance from 1983 to 2005; J. Hydrol. 379 92–110.

Zhang X, Liang S, Zhou G, Wu H and Zhao X 2014Generating global land surface satellite incident short-wave radiation and photosynthetically active radiationproducts from multiple satellite data; Remote Sens. Env-iron. 152 318–332.

Zhang K, Kimball J and Running S 2016 A review ofremote sensing based actual evapotranspiration estima-tion; WIREs Water 3 834–853.

Zhou Y, Kratz D, Wilber A, Gupta S and Cess R 2007An improved algorithm for retrieving surface downwellinglongwave radiation from satellite measurements; J. Geo-phys. Res. 112 D15102:1–D15102:13.

Corresponding editor: Amit Kumar Patra